Signals and Systems For Dummies E-Book

Mark Wickert

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 442

Veröffentlichungsjahr: 2013

Beschreibung

Getting mixed signals in your signals and systems course?

The concepts covered in a typical signals and systems course are often considered by engineering students to be some of the most difficult to master. Thankfully, Signals & Systems For Dummies is your intuitive guide to this tricky course, walking you step-by-step through some of the more complex theories and mathematical formulas in a way that is easy to understand.

From Laplace Transforms to Fourier Analyses, Signals & Systems For Dummies explains in plain English the difficult concepts that can trip you up. Perfect as a study aid or to complement your classroom texts, this friendly, hands-on guide makes it easy to figure out the fundamentals of signal and system analysis.

• Serves as a useful tool for electrical and computer engineering students looking to grasp signal and system analysis
• Provides helpful explanations of complex concepts and techniques related to signals and systems
• Includes worked-through examples of real-world applications using Python, an open-source software tool, as well as a custom function module written for the book
• Brings you up-to-speed on the concepts and formulas you need to know

Signals & Systems For Dummies is your ticket to scoring high in your introductory signals and systems course.

Leseprobe

Signals & Systems For Dummies®

Published byJohn Wiley & Sons, Inc.111 River St.Hoboken, NJ 07030-5774www.wiley.com

Copyright © 2013 by John Wiley & Sons, Inc., Hoboken, New Jersey

Published simultaneously in Canada

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Library of Congress Control Number: 2013934418

ISBN 978-1-118-47581-2 (pbk); ISBN 978-1-118-47566-9 (ebk); ISBN 978-1-118-47582-9 (ebk); ISBN 978-1-118-47583-6 (ebk)

Manufactured in the United States of America

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About the Author

Mark Wickert is a professor of electrical and computer engineering at the University of Colorado, Colorado Springs, Colorado. His teaching focus is signals and systems with an emphasis in communications and signal processing. Mark was previously a board-level designer at Motorola Government Electronics, now a division of General Dynamics.

Mark also works as an industry consultant in digital communications and signal processing for Amergint Technologies LLC. He’s worked with Real Time Logic and developed algorithms for a ZIGBEE radio chip at Atmel Corporation as well.

Mark earned BS and MS degrees in electrical engineering from Michigan Technological University and PhD from Missouri University of Science and Technology (then UMR). He is a member of the Institute of Electrical and Electronics Engineers.

Dedication

To Becki, David, and Paul — my family.

To God be the glory!

Author’s Acknowledgments

This project started with an invitation from my agent, Matt, and a strong dose of encouragement from my wife, Becki, who endured a lot of changes that came with my focus on developing material for this book. My sons, David and Paul, had to accept seeing less of me, too, especially during our summer vacation. Thank you all for your support and encouragement throughout this process.

Thanks, too, to my faculty peers — Greg, Kalkur, and Charlie — for all your encouragement. And I appreciate that Amergint Technologies allowed me do some of the writing at its offices and provided an environment that let me explore the capabilities of Python. Thanks Jeff, Sean, Mark, and Mark.

The staff at Wiley was also very encouraging along the way. I especially want to thank my project editor, Jenny Brown, and my acquisitions editor, Erin Mooney. I know I was stubborn at times, and I am thankful you kept me going. Thanks, too, to copy editor Jennette ElNaggar for making sure my t’s are crossed and i’s are dotted.

Great appreciation goes to Christopher L. Felton, electrical engineer at the Mayo Clinic, for providing the technical review to ensure that the information provided in this book is valuable to the people for whom it’s written. I am also grateful for the help provided by PhD student McKenna Lovejoy, who was willing to jump onboard and provide a fresh eye on this material during the final phases of editing.

To veteran book author, dissertation advisor, fellow faculty member prior to retirement, and still close friend, Rodger Ziemer, thank you for your invaluable support.

Finally, to my dad. Thanks for encouraging my middle-school interest in building electronic gadgets. You spurred my lifelong love for building hardware, software, and countless other things — I’ll always be grateful.

Publisher’s Acknowledgments

We're proud of this book; please send us your comments at http://dummies.custhelp.com. For other comments, please contact our Customer Care Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993, or fax [phone].

Some of the people who helped bring this book to market include the following:

Acquisitions, Editorial, and Vertical Websites

Project Editor: Jenny Larner Brown

Acquisitions Editor: Erin Calligan Mooney

Copy Editor: Jennette ElNaggar

Assistant Editor: David Lutton

Editorial Program Coordinator: Joe Niesen

Technical Editors: Christopher L. Felton

Editorial Manager: Christine Meloy Beck

Editorial Assistant: Alexa Koschier

Cover Photos: © agsandrew/iStockphoto.com

Composition Services

Project Coordinator: Patrick Redmond

Layout and Graphics: Carrie A. Cesavice, Brent Savage, Christin Swinford, Erin Zeltner

Proofreaders: John Greenough, Lauren Mandelbaum, Wordsmith Editorial

Indexer: Steve Rath

Illustrations courtesy of Mark Wickert, PhD

Publishing and Editorial for Consumer Dummies

Kathleen Nebenhaus, Vice President and Executive Publisher

David Palmer, Associate Publisher

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Composition Services

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Signals & Systems For Dummies®

Visit www.dummies.com/cheatsheet/signalsandsystems to view this book's cheat sheet.

Table of Contents

Introduction

About This Book

Conventions Used in This Book

What You’re Not to Read

Foolish Assumptions

How This Book Is Organized

Part I: Getting Started with Signals and Systems

Part II: Exploring the Time Domain

Part III: Picking Up the Frequency Domain

Part IV: Entering the s- and z-Domains

Part V: The Part of Tens

Icons Used in This Book

Where to Go from Here

Part I: Getting Started with Signals and Systems

Chapter 1: Introducing Signals and Systems

Applying Mathematics

Getting Mixed Signals . . . and Systems

Going on and on and on

Working in spurts: Discrete-time signals and systems

Classifying Signals

Periodic

Aperiodic

Random

Signals and Systems in Other Domains

Viewing signals in the frequency domain

Traveling to the s- or z-domain and back

Testing Product Concepts with Behavioral Level Modeling

Staying abstract to generate ideas

Working from the top down

Relying on mathematics

Exploring Familiar Signals and Systems

MP3 music player

Smartphone

Automobile cruise control

Using Computer Tools for Modeling and Simulation

Getting the software

Exploring the interfaces

Seeing the Big Picture

Chapter 2: Brushing Up on Math

Revealing Unknowns with Algebra

Solving for two variables

Checking solutions with computer tools

Exploring partial fraction expansion

Making Nice Signal Models with Trig Functions

Manipulating Numbers: Essential Complex Arithmetic

Believing in imaginary numbers

Operating with the basics

Applying Euler’s identities

Applying the phasor addition formula

Catching Up with Calculus

Differentiation

Integration

System performance

Geometric series

Finding Polynomial Roots

Chapter 3: Continuous-Time Signals and Systems

Considering Signal Types

Exponential and sinusoidal signals

Singularity and other special signal types

Getting Hip to Signal Classifications

Deterministic and random

Periodic and aperiodic

Considering power and energy

Even and odd signals

Transforming Simple Signals

Time shifting

Flipping the time axis

Putting it together: Shift and flip

Superimposing signals

Checking Out System Properties

Linear and nonlinear

Time-invariant and time varying

Causal and non-causal

Memory and memoryless

Bounded-input bounded-output

Choosing Linear and Time-Invariant Systems

Chapter 4: Discrete-Time Signals and Systems

Exploring Signal Types

Exponential and sinusoidal signals

Special signals

Surveying Signal Classifications in the Discrete-Time World

Deterministic and random signals

Periodic and aperiodic

Recognizing energy and power signals

Computer Processing: Capturing Real Signals in Discrete-Time

Capturing and reading a wav file

Finding the signal energy

Classifying Systems in Discrete-Time

Checking linearity

Investigating time invariance

Looking into causality

Figuring out memory

Testing for BIBO stability

Part II: Exploring the Time Domain

Chapter 5: Continuous-Time LTI Systems and the Convolution Integral

Establishing a General Input/Output Relationship

LTI systems and the impulse response

Developing the convolution integral

Looking at useful convolution integral properties

Working with the Convolution Integral

Seeing the general solution first

Solving problems with finite extent signals

Dealing with semi-infinite limits

Stepping Out and More

Step response from impulse response

BIBO stability implications

Causality and the impulse response

Chapter 6: Discrete-Time LTI Systems and the Convolution Sum

Specializing the Input/Output Relationship

Using LTI systems and the impulse response (sequence)

Getting to the convolution sum

Simplifying with Convolution Sum Properties and Techniques

Applying commutative, associative, and distributive properties

Convolving with the impulse function

Transforming a sequence

Solving convolution of finite ­duration sequences

Working with the Convolution Sum

Using spreadsheets and a tabular approach

Attacking the sum directly with geometric series

Connecting the step response and impulse response

Checking the BIBO stability

Checking for system causality

Chapter 7: LTI System Differential and Difference Equations in the Time Domain

Getting Differential

Introducing the general Nth-order system

Considering sinusoidal outputs in steady state

Finding the frequency response in general Nth-order LCC differential equations

Checking out the Difference Equations

Modeling a system using a general Nth-order LCC difference equation

Using recursion to find the impulse response of a first-order system

Considering sinusoidal outputs in steady state

Solving for the general Nth-order LCC difference equation frequency response

Part III: Picking Up the Frequency Domain

Chapter 8: Line Spectra and Fourier Series of Periodic Continuous-Time Signals

Sinusoids in the Frequency Domain

Viewing signals from the amplitude, phase, and frequency parameters

Forming magnitude and phase line spectra plots

Working with symmetry properties for real signals

Exploring spectral occupancy and shared resources

Establishing a sum of sinusoids: Periodic and aperiodic

General Periodic Signals: The Fourier Series Representation

Analysis: Finding the coefficients

Synthesis: Returning to a general ­periodic signal, almost

Checking out waveform examples

Working problems with ­coefficient formulas and properties

Chapter 9: The Fourier Transform for Continuous-Time Signals and Systems

Tapping into the Frequency Domain for Aperiodic Energy Signals

Working with the Fourier series

Using the Fourier transform and its inverse

Getting amplitude and phase spectra

Seeing the symmetry properties for real signals

Finding energy spectral density with Parseval’s theorem

Applying Fourier transform theorems

Checking out transform pairs

Getting Around the Rules with Fourier Transforms in the Limit

Handling singularity functions

Unifying the spectral view with periodic signals

LTI Systems in the Frequency Domain

Checking out the frequency response

Evaluating properties of the frequency response

Getting connected with cascade and parallel systems

Ideal filters

Realizable filters

Chapter 10: Sampling Theory

Seeing the Need for Sampling Theory

Periodic Sampling of a Signal: The ADC

Analyzing the Impact of Quantization Errors in the ADC

Analyzing Signals in the Frequency Domain

Impulse train to impulse train Fourier transform theorem

Finding the spectrum of a sampled ­bandlimited signal

Aliasing and the folded spectrum

Applying the Low-Pass Sampling Theorem

Reconstructing a Bandlimited Signal from Its Samples: The DAC

Interpolating with an ideal low-pass filter

Using a realizable low-pass filter for interpolation

Chapter 11: The Discrete-Time Fourier Transform for ­Discrete-Time Signals

Getting to Know DTFT

Checking out DTFT properties

Relating the continuous-time spectrum to the discrete-time spectrum

Getting even (or odd) symmetry ­properties for real signals

Studying transform theorems and pairs

Working with Special Signals

Getting mean-square convergence

Finding Fourier transforms in the limit

LTI Systems in the Frequency Domain

Taking Advantage of the Convolution Theorem

Chapter 12: The Discrete Fourier Transform and Fast Fourier Transform Algorithms

Establishing the Discrete Fourier Transform

The DFT/IDFT Pair

DFT Theorems and Properties

Carrying on from the DTFT

Circular sequence shift

Circular convolution

Computing the DFT with the Fast Fourier Transform

Decimation-in-time FFT algorithm

Computing the inverse FFT

Application Example: Transform Domain Filtering

Making circular convolution perform linear convolution

Using overlap and add to continuously filter sequences

Part IV: Entering the s- and z-Domains

Chapter 13: The Laplace Transform for Continuous-Time

Seeing Double: The Two-Sided Laplace Transform

Finding direction with the ROC

Locating poles and zeros

Checking stability for LTI systems with the ROC

Checking stability of causal systems through pole positions

Digging into the One-Sided Laplace Transform

Checking Out LT Properties

Transform theorems

Transform pairs

Getting Back to the Time Domain

Dealing with distinct poles

Working double time with twin poles

Completing inversion

Using tables to complete the inverse Laplace transform

Working with the System Function

Managing nonzero initial conditions

Checking the frequency response with pole-zero location

Chapter 14: The z-Transform for Discrete-Time Signals

The Two-Sided z-Transform

The Region of Convergence

The significance of the ROC

Plotting poles and zeros

The ROC and stability for LTI systems

Finite length sequences

Returning to the Time Domain

Working with distinct poles

Managing twin poles

Performing inversion

Using the table-lookup approach

Surveying z-Transform Properties

Transform theorems

Transform pairs

Leveraging the System Function

Applying the convolution theorem

Finding the frequency response with pole-zero geometry

Chapter 15: Putting It All Together: Analysis and Modeling Across Domains

Relating Domains

Using PyLab for LCC Differential and Difference Equations

Continuous time

Discrete time

Mashing Domains in Real-World Cases

Problem 1: Analog filter design with a twist

Problem 2: Solving the DAC ZOH droop problem in the z-domain

Part V: The Part of Tens

Chapter 16: More Than Ten Common Mistakes to Avoid When Solving Problems

Miscalculating the Folding Frequency

Getting Confused about Causality

Plotting Errors in Sinusoid Amplitude Spectra

Missing Your Arctan Angle

Being Unfamiliar with Calculator Functions

Foregoing the Return to LCCDE

Ignoring the Convolution Output Interval

Forgetting to Reduce the Numerator Order before Partial Fractions

Forgetting about Poles and Zeros from H(z)

Missing Time Delay Theorems

Disregarding the Action of the Unit Step in Convolution

Chapter 17: Ten Properties You Never Want to Forget

LTI System Stability

Convolving Rectangles

The Convolution Theorem

Frequency Response Magnitude

Convolution with Impulse Functions

Spectrum at DC

Frequency Samples of N-point DFT

Integrator and Accumulator Unstable

The Spectrum of a Rectangular Pulse

Odd Half-Wave Symmetry and Fourier Series Harmonics

Cheat Sheet

Introduction

Signals and systems is one of the toughest classes you’ll take as an engineering student. But struggling to figure out this material doesn’t necessarily mean you need to sprout early-onset gray hairs and resign yourself to frown lines in your college years. And you definitely don’t want to give up on engineering over this stuff because becoming an engineer is, in my opinion, one of the best career choices you can make. See, you’re no dummy!

This book can help you make sense of the fundamental concepts of signals and systems that may be giving you some static — or even frying your brain. Even better, you can apply the tips and tricks I provide in this book to the courses you’ll take down the line — and right into the real world of computer and electrical engineering!

About This Book

Like all other For Dummies books, Signals & Systems For Dummies isn’t a tutorial. It’s a reference book that you can use as you need it. You don’t need to read each chapter cover to cover (but you may find all the material utterly mesmerizing). You can jump right to the topics or concepts that are giving you trouble, get the help you need, and be on your way with helpful insight to real-world examples of electrical concepts that may be tough to imagine in your textbook of equations.

Conventions Used in This Book

I use the following conventions throughout the text to make things consistent and easy to follow:

New terms appear in italic and are closely followed by an easy-to-understand definition. Variables also appear in italic.

Bold highlights keywords in bulleted lists and the action parts of numbered steps.

Lowercase variables indicate signals that change with time, and uppercase variables indicate signals that are constant. For example, v(t) and i(t) denote voltage and current signals that change with time. If, however, V and I are capitalized, these signals don’t vary in time.

What You’re Not to Read

Although I’m sure you want to read every word of this book, I realize you have other reading material to get through. When you’re short on time and need to just get through the basics, you can skip the sidebars (the shaded boxes sprinkled throughout the book) and paragraphs flagged with a Technical Stuff icon.

Foolish Assumptions

I know you’re a unique kind of brilliant and have one-of-a-kind skills and attributes, but as I wrote this book, I had to make some assumptions about my readers. Here’s what I assume about you:

You’re currently taking an introductory signals and systems course as part of your computer or electrical engineering major, and you need help with certain concepts and techniques. Or you’re planning to take a signals and systems course next semester, and you want to prepare by checking out some supplementary material.

You have a solid handle on algebra and calculus.

You’ve taken an introductory physics class, which exposed you to the concepts of voltage, current, and power in circuits.

You’re familiar with linear differential equations with constant coefficients.

How This Book Is Organized

The study of signals and systems integrates a handful of specific topics from your math and physics courses, and it introduces new techniques to design and manage electrical systems. To help you grasp the core concepts of this electrifying field (sorry, I couldn’t resist) in manageable bites, I’ve split the book into several parts, each consisting of chapters on related topics. Chapters are laid out in an alternation of continuous- and discrete-time topics, starting with the time domain, moving to the frequency domain, and then covering the s- and z-domains.

Additional content, including case studies, is available online at www.dummies.com/extras/signalsandsystems.

Part I: Getting Started with Signals and Systems

This part gives you the signals and systems lingo and an overview of the basic concepts and techniques necessary for tackling your signals and systems course. If you’re already familiar with the fundamentals of how signals and systems operate in the continuous- and discrete-time domains, you can use this part as a refresher.

Part II: Exploring the Time Domain

The focus of these chapters narrows to more closely examine the time domain of signals and systems. In Chapter 7, I introduce differential and difference equation system models, which are used to represent electronic circuits, the audio equalizer on your MP3 music player, filters that separate signals from one another, hybrid systems composed of electrical and mechanical components, and more. I also describe signal and system classifications and properties in these chapters.

Part III: Picking Up the Frequency Domain

The chapters in this part drill down on the frequency domain and the world of system design, particularly wireless systems. Bridging the gap between the continuous- and discrete-time worlds is sampling theory, which is covered in Chapter 10.

Part IV: Entering the s- and z-Domains

This part gets tougher because you’re dealing with the s- and z-domains — a third domain system that engineers use to view the world. Poles and zeros rule here. Signal processing and control systems designers are fond of the s- and z-domains because, for starters, they reduce the mathematics of passing a signal through a system to rather simple algebraic manipulation. From the poles and zeros, you can easily discern system stability and the impact they have on the frequency domain. Great stuff.

Part V: The Part of Tens

Here, get hip to more than ten common mistakes people make when solving problems for signals and systems. Also find a list of ten properties you never want to forget. You may want to print these lists and keep ’em within view.

Icons Used in This Book

To make this book easier to read and simpler to use, I include some icons to help you find key information.

Anytime you see this icon, you know the information that follows is so important that it’s worth recalling after you close this book — even if you don’t remember anything else you read.

This icon appears next to information that’s interesting but not essential. Don’t be afraid to skip these paragraphs.

This bull’s-eye points out advice that can save you time when managing signals and systems.

This icon tries to prevent you from making fatal mistakes in your analysis.

This icon flags worked-through examples in the content so you can find the most practical stuff fast if you’re especially pressed for time.

Where to Go from Here

This book isn’t a novel — although it just may be as intriguing as one. You can start at the beginning and read through to the end, or you can jump in at any chapter to get the information you need on a specific topic. If you need help with calculus and other math basics before dishing out the heartier fare of signals and systems, then pick through Chapter 2 for a quick review. If you just can’t wait another second to find out how the Fourier transform works with different types of signals, then by all means flip to Chapters 9 and 11 right away.

If you’re not sure where to start, or you don’t know enough about signals and systems yet to even wonder about specific topics, no problem — that’s exactly what this book is for. I recommend starting with the chapters in Part I and moving forward from there if you really are a newbie. Then, keep on reading; you’ll be charged up with nitty-gritty details of signals and systems in no time.

Part I

Getting Started with Signals and Systems

Visit www.dummies.com for valuable Dummies content online.

In this part . . .

Find out why computer and electrical engineers need to understand signals and systems analysis.

See how signals and systems function in the worlds of continuous- and discrete-time.

Discover alternative domains used for modeling signals and systems.

Refresh your mathematical know-how and see how algebra, calculus, and trig apply to signals and systems work.

Explore the basic means for assessing the performance of technology-based solutions.